U.S. patent number 7,031,725 [Application Number 10/641,588] was granted by the patent office on 2006-04-18 for method and system for determining relative positions of networked mobile communication devices.
This patent grant is currently assigned to DRS Communications Company, LLC. Invention is credited to C. Britton Rorabaugh.
United States Patent |
7,031,725 |
Rorabaugh |
April 18, 2006 |
**Please see images for:
( Certificate of Correction ) ** |
Method and system for determining relative positions of networked
mobile communication devices
Abstract
Relative positions of a plurality of mobiles communication
devices, which form a wirelessly networked group of mobiles, are
determined at each of the mobiles of the group without the need for
external positioning information obtained from a location remote
from the actual locations of the mobiles of the group. The relative
positions are determined at the mobiles of the group based on
mobile-to-mobile range measurements, distance and direction of
movement measurements and altitude measurements made at the
respective mobiles.
Inventors: |
Rorabaugh; C. Britton (Aldan,
PA) |
Assignee: |
DRS Communications Company, LLC
(Wyndmoor, PA)
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Family
ID: |
31715914 |
Appl.
No.: |
10/641,588 |
Filed: |
August 11, 2003 |
Prior Publication Data
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Document
Identifier |
Publication Date |
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US 20040033808 A1 |
Feb 19, 2004 |
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Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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60402964 |
Aug 13, 2002 |
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Current U.S.
Class: |
455/456.1;
455/404.2; 455/427 |
Current CPC
Class: |
G01S
5/0289 (20130101); H04W 64/00 (20130101); G01S
11/02 (20130101) |
Current International
Class: |
H04Q
7/20 (20060101) |
Field of
Search: |
;455/456.1,456.2,456.3,404.2,407,427,517,67.11,67.1
;342/147,357.06,357.07,357.08,357.09 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Tran; CongVan
Attorney, Agent or Firm: Norris, McLaughlin & Marcus
Parent Case Text
CROSS REFERENCE TO RELATED APPLICATION
This application claims the benefit of U.S. Provisional Application
No. 60/402,964 filed Aug. 13, 2002, assigned to the assignee of
this application and incorporated by reference herein.
Claims
What is claimed is:
1. A method for determining relative positions in three dimensions
of at least four mobile communications devices of a wirelessly
networked group, the method comprising: providing each of the
mobiles of the group with a transceiver for wirelessly
communicating with the transceivers of the other respective mobiles
of the group; measuring ranges between each of the mobiles of the
group and each of the other mobiles of the group respectively,
wherein the measuring is based on propagation time data obtained
from wireless communications between the respective mobiles of the
group; and constructing, based on the ranges, first and second
virtual constellations representative of estimated actual locations
of each of the mobiles of the group, wherein the first
constellation is a mirror image of the second constellation.
2. The method of claim 1 further comprising: measuring, at each of
the mobiles of the group, altitude of the mobile with respect to a
common altitude calibration point; and horizontally orienting the
first and second constellations based on the altitudes.
3. The method of claim 2 further comprising: measuring distance and
direction of movement at each of the mobiles of the group; and
orienting the horizontally oriented first and second constellations
with respect to azimuth based on the distance and direction of
movement of the respective mobiles of the group.
4. The method of claim 3 further comprising: following the
horizontal and azimuth orienting of the first and second
constellations, selecting one of the first and second
constellations as a true image of the relative positions of the
mobiles of the group based on consistency of the directions of the
measured movements of the mobiles of the group.
5. The method of claim 1 further comprising: wirelessly
communicating the range measured between a first of the mobiles and
a second of the mobiles to the first mobile or the second
mobile.
6. The method of claim 2 further comprising: at predetermined
intervals, wirelessly communicating with a time stamp the altitude
measurement at each of the mobiles to each of the other mobiles of
the group.
7. The method of claim 3 further comprising: at predetermined
intervals, categorizing the measured distance and direction of
movement for each of the mobiles as not moving, regular forward
walking or running and motion other than forward walking or running
and wirelessly communicating with a time stamp the movement
categorizations from each of the mobiles in the group to each of
the other mobiles in the group.
8. The method of claim 7 further comprising: at predetermined
intervals, for each of the mobiles having the movement categorized
as forward walking or running, wirelessly communicating with a time
stamp the measured direction and distance of the movement to the
other mobiles in the group.
9. The method of claim 1, wherein the measuring of the ranges
further comprises transmitting at least one of ultrawideband
signals, acoustical ranging signals and optical ranging
signals.
10. The method of claim 1, wherein the measuring of the ranges
further comprises correlating pseudorandom sequences modulated on a
radio frequency carrier signal.
11. The method of claim 3, wherein the transceivers of the
respective mobiles transmit on a wireless communication signal
measured movement, ranges and altitude for the mobiles to each of
the other mobiles of the group.
12. The method of claim 3, wherein the measuring of the movement
further comprises generating time stamped data representative of
detected motion and compass bearing.
13. The method of claim 2, wherein the horizontal orienting of the
virtual constellations further comprises optimizing fit between
measured altitudes of the respective mobiles and altitudes
corresponding to the horizontally oriented virtual
constellations.
14. The method of claim 13, wherein the optimizing the fit includes
performing at least one of a linear least square estimation, a
non-linear least square estimation, a minimum mean squared error
estimation, a method of moments estimation, a maximum likelihood
estimation and a minimum variance estimation.
15. The method of claim 7 further comprising: orienting the virtual
constellations with respect to North for optimizing fit between
measured intervals of regular walking or running motion at at least
one of the mobiles and corresponding virtual movements attributable
to the one mobile based on changes in the estimated
three-dimensional geometric shape of the virtual constellation.
16. The method of claim 7 further comprising: estimating an angular
rotation for orienting the virtual constellations by performing at
least one of a linear least squares estimation, a non-linear least
squares estimation, a minimum mean squared error estimation, a
method of moments estimation, a maximum likelihood estimation and a
minimum variance estimation.
17. The method of claim 3 further comprising: periodically
repeating the measuring of the range, movement and altitude at each
of the mobiles and then repeating the constructing of the first and
second constellations, followed by the horizontal orienting of the
first and second constellations, then followed by the orienting of
the horizontally oriented first and second constellations as to
azimuth and then the selecting of the true image from the
horizontally and azimuthly oriented first and second
constellations.
18. The method of claim 3 further comprising: transmitting the
relative positions of the mobiles of the group to a location remote
from the location of the mobiles of the group.
19. The method of claim 1, wherein one of the mobiles in the group
is in a fixed location.
20. The method of claim 19, wherein the one mobile has global
positioning system capability.
21. The method of claim 19, wherein the fixed location is
substantially at a nexus of communication propagation paths of the
other mobiles in the group.
22. A mobile communications device for determining relative
positions of a group of at least four wirelessly networked mobile
communications devices comprising: a ranging transceiver module and
a data transceiver module for wirelessly communicating with a
ranging transceiver module and a data transceiver module contained
in each of the other respective mobiles of the group, wherein the
ranging transceiver module measures ranges to each of the other
mobiles of the group, wherein the measuring is based on propagation
time data obtained from wireless communications with each of the
other respective mobiles of the group; and a position processing
module for constructing, based on the measured ranges and
mobile-to-mobile ranges generated at each of the other mobiles of
the group and received at the data transceiver module, first and
second virtual constellations representative of estimated actual
locations of each of the mobiles of the group, wherein the first
constellation is a mirror image of the second constellation.
23. The device of claim 22 further comprising: a movement
assessment module for measuring altitude of the mobile with respect
to a common altitude calibration point, and wherein the position
processing module horizontally orients the first and second
constellations based on the measured altitude and altitudes
measured at each of the other mobiles of the group and received at
the data transceiver module.
24. The device of claim 23, wherein the movement assessment module
measures distance and direction of movement, and wherein the
position processing module orients the horizontally oriented first
and second constellations with respect to azimuth based on (i) the
measured distance and direction of movement and (ii) distance and
direction movement measured at each of the other mobiles of the
group and received at the data transceiver module.
25. The device of claim 24, wherein the position processing module,
following the horizontal and azimuth orienting of the first and
second constellations, selects one of the first and second
constellations as a true image of the relative positions of the
mobiles of the group based on consistency of the directions of the
measured movements of the mobiles of the group.
26. The device of claim 22, wherein the data transceiver module
wirelessly communicates the measured range with respect to a first
of the mobiles of the group to at least one of the other mobiles in
the group.
27. The device of claim 23, wherein the data transceiver module, at
predetermined intervals, wirelessly communicates with a time stamp
the altitude measurement to each of the other mobiles of the
group.
28. The device of claim 24, wherein the movement assessment module,
at predetermined intervals, categorizes the measured distance and
direction of movement as not moving, regular forward walking or
running and motion other than forward walking or running and
wherein the data transceiver module wirelessly communicates with a
time stamp the movement categorizations to each of the other
mobiles in the group.
29. The device of claim 28, wherein the data transceiver module, at
predetermined intervals, wirelessly communicates with a time stamp
the measured direction and distance of the movement categorized as
forward walking or running to each of the other mobiles in the
group.
30. The device of claim 22, wherein the ranging transceiver module
transmits at least one of ultrawideband signals acoustical ranging
signals and optical ranging signals for measuring the range.
31. The device of claim 22, wherein the ranging transceiver module
transmits pseudorandom sequences modulated on a radio frequency
carrier signal for measuring the range.
32. The device of claim 24, wherein the data transceiver module
transmits on a wireless communication signal measured movement,
ranges and altitude for the mobiles to each of the other mobiles of
the group.
33. The device of claim 24, wherein the movement assessment module
generates time stamped data representative of detected motion and
compass bearing.
34. The device of claim 23, wherein the position processing module
as part of horizontal orientation of the virtual constellations
optimizes fit between measured altitudes of the respective mobiles
and altitudes corresponding to the horizontally oriented virtual
constellations.
35. The device of claim 34, wherein the optimizing the fit includes
performing at least one of a linear least square estimation, a
non-linear least square estimation, a minimum mean squared error
estimation, a method of moments estimation, a maximum likelihood
estimation and a minimum variance estimation.
36. The device of claim 28, wherein the position processing module
orients the virtual constellations with respect to North for
optimizing fit between measured intervals of regular walking or
running motion at at least of one of the mobiles and corresponding
virtual movements attributable to the one mobile based on changes
in the estimated three-dimensional geometric shape of the virtual
constellation.
37. The device of claim 28, wherein the orienting of the virtual
constellations is achieved by performing at least one of a linear
least square estimation, a non-linear least square estimation, a
minimum mean squared error estimation, a method of moments
estimation, a maximum likelihood estimation and a minimum variance
estimation.
Description
FIELD OF THE INVENTION
The present invention relates generally to determining relative
positions of objects and, more particularly, determining relative
positions of a plurality of wirelessly networked mobile
communications devices without using remotely generated positioning
information.
BACKGROUND OF THE INVENTION
Groups of individuals, such as police officers, firefighters,
rescue workers or soldiers, often need to conduct operations in
built up urban areas. While operating in such areas, the
individuals often find it difficult or impossible to maintain
accurate and updated knowledge of one another's locations because
the structures in an urban area block visual contact between the
individuals. As a result of the inability to establish visual
contact, soldiers in urban environments often become casualties of
friendly fire. Similarly, police officers, firefighters and
soldiers are not able to assist fallen comrades who may be nearby,
yet cannot be visually observed.
Current electronic position location systems do not provide a
satisfactory solution to the problem of providing an individual,
who is part of a group of individuals, with current information as
to the positions of other individuals in the group when the
individuals of the group are located in an urban environment where
visual contact among and between individuals of the group is
difficult or not possible. For example, a global positioning
satellite ("GPS") navigational system typically performs poorly
inside of a building or in an urban canyon. Similarly, a position
determination system for locating cellular phones, such as
developed in accordance with the FCC's E911 initiative, is usually
inadequate because the positioning information generated is of
insufficient accuracy, is limited to a description of location only
in two dimensions and depends upon a sophisticated, fixed
infrastructure that is not always available in the areas in which
many groups will need to conduct operations.
Therefore, a need exists for a system and method for automatically
determining the relative positions of individuals who are members
of a group without the use of positioning information obtained from
an external source that is not part of the group and located
remotely from the area in which the group is positioned.
SUMMARY OF THE INVENTION
In accordance with the present invention, each of a plurality of
mobile communications devices, which can communicate information
wirelessly with one another and form a networked group, determines
its position relative to the other mobiles in the group based on
each of the mobiles' computing its range with respect to each of
the other mobiles or receiving the range information from and
computed at another mobile of the group, monitoring distance and
direction of its movement, monitoring its altitude and obtaining
information from the other mobiles as to their respective altitudes
and movement. Thus, based solely on the range, movement and
altitude information, in other words, without the use of external
positioning information such as global positioning system ("GPS")
satellite information obtained from a location remote from the
positions of the mobiles of the group, each of the mobiles
determines its relative distance and bearing with respect to each
of the other mobiles in the group.
In a preferred embodiment, each mobile of a wireless networked
group of mobile includes a position processing module processor
coupled to wireless data and ranging transceiver modules. The
ranging transceiver module communicates wirelessly with the ranging
transceiver module of each of the other networked mobiles to obtain
information for computing the range between its mobile and each of
the other mobiles in the group. A position processing module in
each of the mobiles uses the ranges to construct a virtual
constellation of the actual positions of the networked mobiles and
a virtual constellation of a reflection of the actual positions
virtual constellation. A movement assessment module in each of the
mobiles monitors distance and direction of movement of the mobile.
The movement assessment module also measures altitude of the
subject mobile with respect to a common calibration point, in view
of altitude data received from the other networked mobiles at the
data transceiver module. The position processing module uses the
movement (distance and direction) data collected at its mobile and
received at the data transceiver module from the other mobiles to
resolve any potential reflective ambiguity concerning the two
possible constellations, thereby identifying the true constellation
shape. In a preferred embodiment, the position processing module
uses the altitude data to orient the true constellation with
respect to the true horizontal plane. In a further preferred
embodiment, the position processing module uses the distance and
direction data to orient the true constellation with respect to
azimuth. The resulting oriented true constellation represents the
relative positions, i.e., the oriented geometric shape, of all of
the mobiles within the networked group.
BRIEF DESCRIPTION OF THE DRAWINGS
Other objects and advantages of the present invention will be
apparent from the following detailed description of the presently
preferred embodiments, which description should be considered in
conjunction with the accompanying drawings in which like references
indicate similar elements and in which:
FIG. 1 is a perspective view of a group of individuals dispersed in
a building.
FIG. 2 is an illustration of a group of individuals, each of which
is carrying a mobile communications device in accordance with a
preferred embodiment of the present invention, as a constellation
of points in three-dimensional space.
FIG. 3 is a functional block diagram of a mobile communications
device in accordance with a preferred embodiment of the present
invention.
FIG. 4 is a flow diagram of a process for determining relative
positions of a group of networked mobile communications devices in
accordance with the present invention.
FIGS. 5A and 5B are true and mirror images, respectively, of a
virtual constellation of the positions of the individuals of FIG.
2.
FIG. 6 is a flow diagram of a process for determining the geometric
shape defined by the actual positions of a group of networked
mobiles in accordance with the present invention.
FIG. 7 is a flow diagram of a process for horizontally orienting
estimated geometric shapes of a group of networked mobiles in
accordance with the present invention.
FIG. 8 is a flow diagram of a process for orienting estimated
geometric shapes of a group of networked mobiles with respect to
azimuth.
FIG. 9A is constellation representative of the individuals of FIG.
2 before movement of the mobile A.
FIG. 9B is a constellation representative of the individuals of
FIG. 2 after movement of the mobile A.
FIGS. 10A 10D are illustrations of the true image and mirror image
virtual constellations of FIG. 2, respectively, oriented based on
movement data processing in accordance with the present
invention.
DETAILED DESCRIPTION OF THE INVENTION
In accordance with the present invention, relative positions of
individuals in a group, where each individual carries a mobile
communications device for wirelessly communicating with each of the
other individuals to form a group of networked mobiles, are
determined at each of the mobiles without the use of external
positioning information, such as GPS information, which oftentimes
is unavailable at various locations where the group may be
operating. FIG. 1 illustrates how a group of individuals A, B, C
and D, such as police officers, firefighters, guards or soldiers,
may be dispersed to locations in and around a multistory building,
which is a typical environment in which GPS-based or like external
electronic signal positioning systems may perform poorly or fail
completely. If the position of each individual is represented as a
point, the formation of the group can be viewed as a constellation
of points in space as shown in FIG. 2. At any instant in time, the
locations of the individuals uniquely define the three-dimensional
shape of the true constellation. For purposes of illustrating the
features of the present invention, it is assumed that each of the
individuals in FIG. 2 carries a mobile communications device
constructed and functioning in accordance with the present
invention.
In accordance with a preferred embodiment of the present invention,
the relative positions of individuals in a mobile networked group
are determined at a mobile communications device 101 carried by
each of the individuals in the group so long as the group includes
at least four networked mobiles 101. The relative positions
determination is performed at one mobile of the group based on
collection of mobile-to-mobile range data, mobile movement data and
altitude data at the one mobile, and receipt of altitude and
movement data transmitted to the one mobile from each of the other
mobiles in the group. Each of the mobiles uses the collected and
received data to construct a virtual constellation having the same
shape and orientation as the true constellation corresponding to
the relative positions of the mobiles in the group.
FIG. 3 is a preferred embodiment of the mobile 101 in accordance
with the present invention. Referring to FIG. 3, the mobile 101
includes a ranging transceiver module 102, a movement assessment
module 103, a data transceiver module 104, a position processing
module 105 and a position display module 106. The data transceiver
module 104 is coupled to each of the ranging transceiver module
102, the movement assessment module 103 and the position processing
module 105. The position processing module 105 is coupled to the
position display module 106 and the movement assessment module 103.
The ranging module 102 is coupled to an antenna 120 and the data
transceiver module 104 is coupled to an antenna 122. It is to be
understood that each of the modules of the inventive mobile 101,
which are described below as performing data processing operations,
constitutes a software module or, alternatively, a hardware module
or a combined hardware/software module. In addition, each of the
modules suitably contains a memory storage area, such as RAM, for
storage of data and instructions for performing processing
operations in accordance with the present invention. Alternatively,
instructions for performing processing operations can be stored in
hardware in one or more of the modules. Further, it is to be
understood that, in accordance with the present invention, the
modules of the mobile 101 can be combined, as suitable, into
composite modules. Also, the antennae 120 and 122, which are
conventional devices well known in the prior art, can be combined
into a single integral antenna, as is also well known in the
art.
The ranging transceiver module 102, which includes a conventional
wireless, such as a radio frequency ("RF") signal, receiver and
transmitter, collects data for determining the distance between the
mobile in which it is contained and each of the other mobiles in
the networked group. In a preferred embodiment, the transceiver
module 102 establishes, via the antenna 120, a radio ranging link
107 between itself and the transceiver module 102 of another
mobile. Based on the radio raging links, the transceiver module 102
of the subject mobile measures the signal transit time between
itself and the ranging transceiver modules of other respective
mobiles in the group. From the signal time transit data, the range
between two mobiles is readily computed using well known
techniques.
In a preferred embodiment, the ranging transceiver module uses an
RF carrier modulated by a high rate PN sequence for ranging. In
another preferred embodiment, the signal used for ranging is an
ultrawideband ("UWB") signal. UWB is advantageous because: (1) it
provides virtually infinite frequency diversity, thus ensuring that
the ranging signal can penetrate a wide variety of common building
materials; (2) UWB signals have a low probability of detection and
intercept; (3) the narrow pulse widths (500 psec) used in UWB
allows for ranging accuracies to less than one foot; (4) and UWB
signals can be used anywhere in the world without having to fit
into or coordinate with local civilian and military frequency
allocation plans.
The movement assessment module 103 includes an electronic compass
and measures movement of the subject mobile in terms of distance
and direction. In a preferred embodiment, the module 103 determines
whether the mobile is not moving, moving in an unknown direction or
moving in a known direction. In cases where a mobile is moving in a
known direction, the movement assessment module 103 determines the
direction. Further, the movement assessment module 103 measures the
altitude of the subject mobile with respect to a reference altitude
that is set when the mobile is initialized for use. In a preferred
embodiment, the module 103 includes a barometric altimeter, such as
commonly included in a Swiss army watch or portable GPS receivers,
that uses pressure differences to measure relative altitude with
respect to the altitude of a common calibration point which is set
as the reference altitude.
The data transceiver module 104, which includes a conventional
wireless, such as an RF signal, receiver and transmitter,
exchanges, via the antenna 122, information between itself and the
data transceiver modules 104 of other networked mobiles of the
group. The data module 104 at each mobile transmits its altitude
and movement measurements to the other mobiles via wireless data
links 108 established between itself and the data transceiver
modules 104 of the various mobiles. In a preferred embodiment where
a ranging transceiver module of a subject mobile cannot directly
measure mobile-to-mobile distance to another mobile, that other
mobile, or alternatively another of the mobiles of the group,
conveys this ranging information to the subject mobile over a
wireless data link 108 established between its data transceiver
module and the data transceiver module 104 of the subject
mobile.
The position processing module 105 retrieves the ranging data from
the module 102, the movement and altitude data collected at the
module 103 and any range and the altitude data received at the
module 104 to compute, as discussed in detail below, the relative
positions of the networked mobiles.
The position display module 106 displays the relative positions of
the networked mobiles which are computed at the processing module
105. In a preferred embodiment, the module 106 includes a display
unit resembling an oversized ruggedized PDA. In a further preferred
embodiment, the module 106 is not included in selected mobiles of a
group.
In a preferred embodiment, the mobile of the present invention
includes a first component structure, which does not include the
antennae 120 and 122 and the movement assessment module 103, is
approximately the size of a cordless telephone handset and is
configured to be worn on or attached to an article of clothing. The
movement assessment module 103 is embodied as a second component
structure, preferably the same size or smaller than a cordless
telephone handset and configured for attachment to a belt or belt
loops on pants. The antennae 120 and 122 are embodied as a third
component structure, preferably readily attachable to a shirt
collar. The first, second and third component structures of the
mobile are electronically coupled to one another. In a further
preferred embodiment, the mobile component structures are
configured to be carried in a holster to provide for easy removal
for use.
In another preferred embodiment, the position display module 106
contains an electronic compass module (not shown). The compass
module includes an electronic compass, which is a different
electronic compass than the electronic compass included in the
movement assessment module 103. The compass module processes the
relative position data generated by the module 105 and suitably
provides control signals to the display module 106 so that a
graphical display of the computed relative positions is rotated to
orient the displayed relative positions with the corresponding
features in the actual environment, even if the display is pointed
in different directions.
FIG. 4 is a high level flow process 150 illustrating measurement
and collection of data and computations performed at each of the
mobiles of a group of wirelessly networked mobiles, in accordance
with the present invention, to determine the relative positions of
the mobiles of the group. For purposes of illustrating the process
150 and the processes corresponding to steps of the process 150
which are described in further detail in the text accompanying the
description of FIGS. 6 8, reference is made to the individuals A,
B, C and D shown in FIG. 2 each of whom is carrying a mobile 101.
Also, for ease of reference, the individuals of the group shown in
FIG. 2 are referred to below as mobiles A, B, C, and D. It is also
assumed that each of the mobiles 101 is in the form of a three
part, electronically coupled unit including (i) a first unit of a
movement assessment module 103, which is worn on the belt of an
individual to ensure that an accelerometer within the movement
assessment module 103 can sense foot steps, i.e., movement; (ii) a
second unit of the antennae 120 and 122, which is worn on an upper
portion of an individual's body to maximize signal transmission and
reception capability; and (iii) a third unit containing the modules
102, 104, 105 and 106 and which can be worn virtually anywhere on
the body of an individual.
Referring to FIG. 4, in step 152, each ranging transceiver module
102 measures mobile-to-mobile distance with respect to each of the
mobiles in the group and stores in its memory the range with an
associated time stamp. Alternatively, in step 152, the data
transceiver module 104 in a first mobile, such as the mobile A,
receives time stamped mobile-to-mobile range data from a second
mobile, such as the mobile B or alternatively the mobiles C or D,
based on mobile-to-mobile distance measurements made by the second
mobile B with respect to first mobile A.
In step 154, the position processing module 105 uses the locally or
the remotely measured mobile-to-mobile distances to computer a
mirror-image pair of geometric shapes or virtual constellations
201A and 201B. One of the constellations is congruent to the actual
true geometric shape 205 defined by the positions of the individual
mobiles within the group and shown in FIG. 4 at step 160, which is
discussed in detail below. In other words, based solely on the
mobile-to-mobile range information, a mobile computes a virtual
constellation of the estimated positions that has the same shape as
the true constellation of the actual positions of the mobiles of
the group. Thus, the range information permits that, to within a
reflection, the geometric shape defined by the positions of the
individual mobiles within the group can be determined.
The virtual constellation that the position processing module 105
in a mobile determines based on the mobile-to-mobile range
information is in an arbitrary orientation that exhibits yaw,
pitch, and roll with respect to the orientation of the true
constellation. It is not possible to determine the orientation
(yaw, pitch, roll) or absolute position (x, y, z) or (latitude,
longitude, altitude) of this geometric shape solely based on the
range information. The virtual constellation has an unobservable
virtual North-South ("N-S") axis such that, when the virtual
constellation is correctly oriented with respect to the true
constellation, the virtual N-S axis will be parallel to the true
N-S axis. Yaw is the angle, measured in the horizontal plane,
between the true and virtual N-S axes. Similarly, the virtual
constellation has an unobservable virtual up-down (U-D) axis, such
that when the constellation is correctly oriented, the virtual U-D
will be parallel to the true U-D axis. Pitch is the angle, measured
in the vertical North-South plane, between the true and virtual U-D
axes. Roll is the angle, measured in the verical East-West plane,
between the true and virtual U-D axes.
Steps 156, 158 and 160 of the process 150 provide, in accordance
with the present invention, that any potential reflective ambiguity
of the two constellations is resolved and that the proper
orientation of the geometric shape is determined without the use of
GPS information. In step 156, the position processing module 105 in
each of the mobiles collects movement and altitude data and stores
such data with an associated time stamp in its memory. In addition,
the mobiles of a group share their respective movement and altitude
measurement data with one another via the wireless communication
links 108 generated by the respective data transceiver modules
104.
In step 158, the position processing module 105 uses the locally
and the remotely measured altitude data to determine, for each of
the two images corresponding to the pair of virtual constellations,
the proper orientation with respect to the horizontal plane. The
result of applying horizontal orientation processing is a
mirror-image pair of virtual constellations 203A and 203B which are
oriented in pitch and roll.
In step 160, each position processing module 105 uses the locally
and the remotely measured movement data to select the correct image
from the mirror-image pair of virtual constellations and to
determine the proper orientation of the selected image with respect
to azimuth. In step 162, the position display module 106 provides
output representative of the relative positions of the mobiles of
the group, which were determined in step 160, on a monitor
device.
In a preferred embodiment, the mobile continuously tracks the
positions of the individuals within the group and displays these
positions on a handheld device that resembles a large PDA. In a
further preferred embodiment, the position processing module 105
routes the relative positions data representative of the true
constellation to the data transceiver module 104 and the module 104
transmits, via the antenna 122, the relative positions of the
mobiles to a remote command post.
Determining the Geometric Shape Defined by the Actual Positions of
the Mobiles
Referring again to FIG. 4, in step 152 the ranging transceiver
module 102 in each mobile of the group communicates with each of
the other mobiles in the group to determine straight-line distance
between the subject mobile and each of the other mobiles. For
example, the ranging transceiver module in mobile A transmits a
time encoded wireless signal, such as an RF signal, to the mobile
B. Based on this transmission, the ranging transceiver module of
the mobile B can measure the time it takes for an RF signal to
propagate from the ranging transceiver module of the mobile A to
the ranging transceiver module of the mobile B. After the ranging
transceiver module 102 in the mobile B collects the suitable
propagation time data, its data transceiver module 104 transmits
this propagation time data to the data transceiver module 104 of
the mobile A on an RF carrier signal. The mobiles A, B, C and D in
the group, thus, in step 152 operate cooperatively in a network to
collect the propagation time data necessary for determining the
distances from each mobile to every other mobile in the group.
In step 154, based on the propagation time data collected for each
of the mobiles, the position processing module at a mobile, for
example the mobile A, computes the distance between the mobile A
and each of the mobiles B, C and D. Based only on the
mobile-to-mobile distance measurements at each of the mobiles of
the group, and without any known fixed reference positions, the
position processing module constructs a mirror-image pair of
geometric shapes or virtual constellations which are defined by the
positions of the individual mobiles within the group. If the
distance measurements are exact, the pair of shapes will match
exactly. In a practical system, however, some measurement error is
likely. Preferably, the virtual constellations have a shape that is
an optimal estimate of the shape of the true constellation of the
actual positions of the mobiles of the group.
FIGS. 5A and 5B illustrate, respectively, a true image
constellation 203A and a mirror image constellation 203B for the
mobiles A, B, C and D as shown in FIG. 2. The constellation 203A,
which for purposes of the example is the true geometric shape,
matches the actual geometric shape of all of the mobiles in the
group. Referring to FIG. 5A, which is the image of the virtual
constellation pair representative of the true constellation
corresponding to the mobiles shown in FIG. 2, the sequence of
mobiles D, C and B is clockwise when viewed from mobile A. In the
reflected image shown in FIG. 5B, the sequence of mobiles D, C and
B is counterclockwise when viewed from mobile A.
In a preferred embodiment, the position processing module of a
mobile, using the collected range information which has some
measurement error, performs a linearized least squares computation
to estimate the geometric shape defined by the positions of the
various mobiles within a group. The use of a least squares
computation generates an optimal estimate of the geometric shape in
the presence of imperfect range measurements, because this estimate
has the least squared range error of all the possible estimates
that can be made from a set of imperfect measurements. The position
processing module arbitrarily establishes a local coordinate system
to facilitate the estimation. Within this local coordinate system,
a pair of mobiles or nodes designated node N.sub.P and node N.sub.Q
are located respectively at coordinate positions (x.sub.P, y.sub.P,
z.sub.P) and (x.sub.Q, y.sub.Q, z.sub.Q). The estimated range
between N.sub.A and N.sub.B can be calculated as .rho..sub.PQ=
{square root over
((x.sub.Q-x.sub.P).sup.2+(y.sub.Q-y.sub.P).sup.2+(z.sub.Q-z.sub.P).sup.2)-
}{square root over
((x.sub.Q-x.sub.P).sup.2+(y.sub.Q-y.sub.P).sup.2+(z.sub.Q-z.sub.P).sup.2)-
}{square root over
((x.sub.Q-x.sub.P).sup.2+(y.sub.Q-y.sub.P).sup.2+(z.sub.Q-z.sub.P).sup.2)-
} (1) The linear least squares computation requires an equation for
range estimation error that is linear in the coordinates. Equation
(1) can be linearized by generating a truncated Taylor series
expansion about the estimated positions (x.sub.P, y.sub.P, z.sub.P)
and (x.sub.Q, y.sub.Q, z.sub.Q). The series is truncated to
eliminate all second and higher order terms to yield
.rho..rho..times..differential..rho..times..differential..rho..times..dif-
ferential..rho..times..differential..rho..times..differential..rho..times.-
.differential. ##EQU00001## where r.sub.PQ is the measured range
between node N.sub.P and node N.sub.Q. It is convenient to define
the range estimation error as R.sub.PQ=.rho..sub.PQ-r.sub.PQ and
restate Equation (2) as
.times..rho..times..differential..rho..times..differential..rho..times..d-
ifferential..times..rho..times..differential..rho..times..differential..rh-
o..times..differential. ##EQU00002##
In a preferred embodiment, the shape is estimated by using the
positions of three mobiles to define the axes of the local
coordinate system in a particular way. The local node, i.e., the
particular mobile performing the estimation, designated node
N.sub.0, is placed at the origin of the local coordinate system so
that x.sub.0=0, y.sub.0=0 and z.sub.0=0. The first remote node that
the local node is able to range is designated as node N.sub.1. This
node is placed on the positive x axis of the local coordinate
system so that y.sub.1=0 and z.sub.1=0, and the range estimation
error Equation (3) for N.sub.0 and N.sub.1simplifies to
.rho..times..differential. ##EQU00003## The second remote node that
the local node is able to range is designated as node N.sub.2. This
node is placed in the x-y plane of the local coordinate system, so
z.sub.2=0 and the range estimation error for N.sub.0 and N.sub.2
simplifies to
.rho..times..differential..rho..times..differential. ##EQU00004##
The range estimation error for N.sub.1 and N.sub.2 simplifies
to
.rho..times..differential..rho..times..differential..rho..times..differen-
tial. ##EQU00005##
Once the local coordinate system is fixed by the positions of the
local node and the first two remote nodes, the positions of all
other remote nodes are not constrained with respect to the local
coordinate axes. The range estimation error from one unconstrained
remote node to another will include all six terms shown in Equation
(3). The range estimation error from node No to an unconstrained
node simplifies to the form
.rho..times..differential..rho..times..differential..rho..times..differen-
tial. ##EQU00006## The range estimation error from node N.sub.1 to
an unconstrained node simplifies to the form
.rho..times..differential..rho..times..differential..rho..times..differen-
tial..rho..times..differential. ##EQU00007## The range estimation
error from node N.sub.2 to an unconstrained node simplifies to the
form
.rho..times..differential..rho..times..differential..rho..times..differen-
tial..rho..times..differential..rho..times..differential.
##EQU00008## The system of equations for range estimation error can
be put in matrix form as R=.alpha.d (4) where
.times..times..times..times..times..differential..differential..different-
ial..differential..differential..differential..differential..differential.-
.differential..times..times..times..alpha..alpha..alpha..alpha..alpha..alp-
ha..times. ##EQU00009## and the submatrices .alpha..sub.0 through
.alpha..sub.N-2 are configured as shown below
.alpha. ##EQU00010##
.alpha..rho..rho..rho..rho..rho..rho..rho..rho..rho..rho..rho.
##EQU00010.2##
.alpha..rho..rho..rho..rho..rho..rho..rho..rho..rho..rho..times..rho..rho-
..times..times..rho..rho..rho. ##EQU00010.3##
.alpha..rho..rho..rho..rho..rho..rho..rho..rho..rho..rho..rho..rho..rho..-
rho..rho..rho..rho..rho. ##EQU00011## For the general case of
N>2 nodes, the number of range equations will be
.function. ##EQU00012## and the number of unknown coordinates will
be N.sub.unk=3(N-2) The system of equations will be overspecified
for systems involving five or more nodes. When the system is
overspecified, the best solution in a least squares sense can be
found using the normal equation to solve Equation (4) for d where
d=[.alpha..sup.T.alpha.].sup.-1.alpha..sup.TR (6)
In a preferred embodiment, the position processing module 105 in a
mobile, at step 154 of the process 150, performs a computation
process 200, as shown in FIG. 6, to construct the virtual
constellations. Referring to FIG. 6, in step 202, the position
processing module 105 assumes a set of starting position estimates
(x,y,z) for each of the nodes in the group. Node N.sub.o is
constrained to lie at (0,0,0). Node N.sub.1 is started at
(r.sub.max,0,0) where r.sub.max is the maximum distance at which
ranging can be performed. Node N.sub.2 is started at
(r.sub.max,r.sub.max,0) and all other nodes are started at
(r.sub.max,r.sub.max,r.sub.max).
In step 204, the position processing module 105 computes an
estimated range for each pair of nodes i and j .rho..sub.i,j=
{square root over
((x.sub.i-x.sub.j).sup.2+(y.sub.i-y.sub.j).sup.2+(z.sub.i-z.sub.j).sup.2)-
}{square root over
((x.sub.i-x.sub.j).sup.2+(y.sub.i-y.sub.j).sup.2+(z.sub.i-z.sub.j).sup.2)-
}{square root over
((x.sub.i-x.sub.j).sup.2+(y.sub.i-y.sub.j).sup.2+(z.sub.i-z.sub.j).sup.2)-
} (1) and forms the a matrix in accordance with Equation (5) and
the equations for the submatrices .alpha..sub.0 through
.alpha..sub.N-2 discussed above.
In step 206, the position processing module 105 forms the range
estimation error vector from the differences between the estimated
ranges and the corresponding measured ranges
R.sub.i,j=.rho..sub.i,j-r.sub.i,j
In step 208, the position processing module 105 uses the a matrix
from step 204 and the range error vector R from step 206 to compute
the position adjustment vector d as
d=[.alpha..sup.T.alpha.].sup.-1.alpha..sup.TR (6)
In step 210, the position processing module 105 applies the
adjustment values in d to the corresponding estimates
(x.sub.k).sub.new=(x.sub.k).sub.old+.differential.x.sub.kK=1,2, . .
. , N-1
(y.sub.k).sub.new=(x.sub.k).sub.old+.differential.x.sub.kK=2,3, . .
. , N-1
(z.sub.k).sub.new=(x.sub.k).sub.old+.differential.X.sub.kK=3,4, . .
. , N-1
In step 212, the position processing module 105 repeats steps 202,
204, 206, 208 for a predetermined number of iterations or until the
RMS value of the adjustment vector falls below some predetermined
threshold. In step 212, the estimated positions
(x.sub.k,y.sub.k,z.sub.k) are the estimated positions of the nodes
which define one image of the mirror-image pair of geometric shapes
corresponding to the shape defined by the positions of the
individual mobiles within the group, such as shown in FIG. 5A. The
position processing module 105 generates a second image in the
mirror-image pair, such as shown in FIG. 5B, by negating either the
x, y, or z coordinate in every node position
(x.sub.k,y.sub.k,z.sub.k). Negating every x coordinate reflects the
image through the y-z plane. Negating every y coordinate reflects
the image through the x-z plane. Negating every z coordinate
reflects the image through the x-y plane. As the local coordinate
system is arbitrary, any one of these reflections can be utilized
as the second image in the mirror-image pair.
Horizontal Orientation of the Virtual Constellation
In accordance with the present invention, altitude data measured at
each of the mobiles and then communicated to the other mobiles of
the networked group is used in step 158 or the process 150 to
orient the virtual constellation, such as determined by the process
200 performed at step 154 of the process 150, with respect to the
true horizontal plane. The virtual constellation is rotated in
virtual space to find the orientation of the virtual constellation
that results in the best fit of virtual relative altitudes to
measured relative altitudes. In this orientation, the pitch and
roll of the virtual constellation is approximately zero. For ease
of reference herein, a virtual constellation that has been so
aligned is referred to as a pitch-and-roll aligned ("PRA")
constellation. The optimization of the fit is preferably performed
using at least one of a linear least squares estimation, a
non-linear least squares estimation, a minimum mean squared error
estimation, a method of moments estimation, a maximum likelihood
estimation and a minimum variance estimation, which are well known
mathematical techniques for optimizing an estimation.
FIG. 7 illustrates an exemplary process 250 for horizontally
orienting the pair of mirror image constellations obtained in
accordance with the present invention based on altitude data
collected at the movement assessment module at each mobile of a
networked group and without using any GPS fixes. Referring to FIG.
7, in step 252 the position processing module 105 of a mobile, such
as the mobile A of FIG. 2, defines a virtual constellation of N
discrete points in three-dimensional space in the form of an
N.times.3 matrix C. Each row of C represents one point, and the
column entries are the x, y, and z coordinates of the points.
In step 254, the position processing module 105 rotates the
original constellation about the x and y axes to generate a vector
of rotated z coordinates, where the z coordinates of the rotated
constellation are a good match for the measured altitudes of the
corresponding nodes in the actual deployment of the mobiles. If the
rotation angle about the x axis is .theta., and the rotation angle
about the y axis is .phi., then the vector of rotated z coordinates
can be obtained from C as z=Ct.sub.2 (7) where
.times..times..PHI..times..times..theta..times..times..times..times..PHI.-
.times..times..theta..times..times..times..times..PHI.
##EQU00013##
In step 256, the position processing module 105 of the mobile, such
as the mobile A, references the measured altitudes of the other
mobiles, such as the mobiles B, C and D, to the measured altitude
of the mobile A to compute the optimal rotation by finding the
least squares solution for t.sub.z in z.sub.m=Ct.sub.2 where
z.sub.m is the vector of measured altitudes referenced to the
measured altitude of the local mobile unit. This solution is
readily found as t.sub.z=[C.sup.TC].sup.-1C.sup.Tz.sub.m (8) and
the result obtained from Equation (8) will be a three-element
column vector
##EQU00014##
In step 258, the position processing module 105 solves for .phi. as
.phi.=sin.sup.-1 .alpha. For -1<a <1, the equation a =sin
.phi. has two solutions for .phi. in the range -.pi. to .pi.. If
this primary value is designated as .phi..sub.0, then the second
value can be obtained as
.PHI..pi..PHI..PHI..gtoreq..pi..PHI..PHI.< ##EQU00015## For
-1<b <1, the equation b =sin .theta.cos .phi. will have four
solutions for .theta. in the range -.pi. to .pi.. There will be two
solutions for .theta.for each of the two possible values of
.phi.:
.theta..times..times..times..PHI..theta..pi..theta..theta..gtoreq..pi..th-
eta..theta.<.theta..times..times..times..PHI..theta..pi..theta..theta..-
gtoreq..pi..theta..theta.< ##EQU00016## The original virtual
constellation is double-rotated four different ways corresponding
to the four different combinations of .phi. and .theta.:
(.phi..sub.0, .theta..sub.0), (.phi..sub.0,.theta..sub.1),
(.phi..sub.1, .theta..sub.2) and (.phi..sub.1, .theta..sub.3). The
double-rotation that results in the smallest mean-squared altitude
error is deemed to be the correct rotation. Orienting the Virtual
Constellation with Respect to Azimuth
Continuing with the illustrative example, it is assumed that the
horizontal orientation procedures described above have already been
applied to the mirror-image pair of virtual constellations to
produce the oriented pair of virtual constellations 203A and 203B,
as shown in FIGS. 5A and 5B, respectively, which are pitch-and-roll
aligned. In accordance with the present invention, the virtual
constellations 203 are subsequently rotated around the z axis to
bring virtual azimuths observed in the constellations into
alignment with azimuths measured in the actual deployment of the
mobiles of the group to yield a single virtual constellation 205
that is properly oriented in yaw, pitch and roll.
It is noted that resolution of mirror-image ambiguity in the
virtual constellations can be readily performed based on prior art
techniques for determining the yaw of the PRA constellation
relative to the true constellation if mobiles at three or more
different latitude and longitude positions, which do not all lie in
a straight line, can obtain GPS location fixes. A GPS receiver, by
itself, must be able to receive the direct path signal from at
least four satellites in the GPS constellation to obtain a GPS
location fix. The three GPS fixes define a triangle in which the
three fix points are in a particular sequence when viewed from
above. As the two GPS fixes define a line of known length and
azimuth, the virtual PRA constellation can be virtually rotated
until the corresponding virtual line has the same azimuth as the
line defined by the GPS fixes. The corresponding points in the
virtual constellation proceed in the same sequence in the correct
image and in the reverse sequence in the incorrect image. By
examining these sequences in both images, the image that yields the
reversed sequence is readily discarded.
In an alternative preferred embodiment, the networked mobiles of a
group further include GPS capability and exchange information as to
their relative positions with respect to the other mobiles of the
group. Two GPS receivers working cooperatively can each obtain a
position fix when, together, they can receive the direct path from
as few as three satellites, provided that there are a total of at
least five receivable satellite-to-receiver direct paths. See
"Method and System for Determining Absolute Positions of Mobile
Communications Devices Using Remotely Generated Positioning
Information," U.S. Ser. No. 10/639,022, filed Aug. 11, 2003 and
assigned to the assignee of this application, incorporated by
reference herein.
A flow process 300 for orienting the horizontally oriented virtual
constellations with respect to azimuth without GPS information, and
based on movement measurements in accordance with the present
invention, thereby identifying a single virtual constellation
oriented in yaw, pitch and roll, such as the relative positions of
the mobiles A, B, C and D, is shown in FIG. 8.
In a preferred embodiment, the movement assessment module 103
includes an electronic pedometer, such as described in U.S. Pat.
No. 5,583,776, incorporated by reference herein, as well as an
electronic compass and a barometric altimeter. The movement
assessment module 103 uses the pedometer in conjunction with the
compass to determine the distance and direction the mobile moves
when the individual carrying the mobile walks or runs in a forward
direction, as such forward movements generally are accurate
measurements of movement. The movement assessment module 103
distinguishes when the individual is stationary or moving in some
manner other than forward walking or running and discards these
measurements. Thus, unlike the prior art technique of using pure
dead reckoning to measure movement, which requires estimating the
direction and distance of movement other than forward walking or
running, the present invention tracks mobile positions without
requiring accurate estimates of direction and distance traveled
when the individual is moving in some manner other than normal
forward walking or running.
In a preferred embodiment, the movement assessment module includes
an altimeter, a solid state electronic compass and three
accelerometers. One of the accelerometers is mounted vertically and
configured to act as a pedometer for detecting the foot impacts
generated while walking, as is known in the art. The other two
accelerometers are mounted horizontally, one oriented front-to-back
and the other one oriented left-to-right. The measurements
performed at the horizontal accelerometers are used to screen the
foot impact indications provided by the vertical accelerometer to
provide that normal forward walking or running can be distinguished
from all other movements. During periods of normal forward
movement, the average azimuth indicated by the electronic compass
is a good estimate of the direction of travel.
For example, when an individual walks or runs in a forward
direction, this movement is evidenced in the virtual constellation
as a change from the constellation shape before the movement to the
constellation shape after the movement. The virtual constellation
can be rotated around the z axis until the line of apparent
movement coincides with the compass-measured direction of the
motion of the individual. FIG. 9A illustrates the original
constellation 203A of the mobiles A, B, C and D of FIG. 2 before
movement, and FIG. 9B illustrates a constellation 203AA in which
the mobile A has moved while the mobiles B, C, and D remain fixed.
As described below in connection with the process 300 illustrated
in FIG. 8, the constellation corresponding to the end of the
movement interval is rotated in azimuth until the movement vector
of the individual has a virtual azimuth that agrees with the
azimuth measured by the electronic compass in the mobile of the
individual. The rotation effectively orients the entire
constellation for all of the individuals in the group. It is noted
that any single measurement will include some measurement error
and, therefore, in a preferred embodiment, the computation includes
a best-fit rotation based on multiple simultaneous movements
reported by different mobiles. In a further preferred embodiment,
the optimal rotation for a single yaw adjustment opportunity is
found using least squares estimation techniques. In alternative
preferred embodiments, an angular rotation is estimated for
orienting the horizontally oriented virtual constellation by
performing at least one of a linear least squares estimation, a
non-linear least squares estimation, a minimum mean squared error
estimation, a method of moments estimation, a maximum likelihood
estimation and a minimum variance estimation, which are well know
techniques for optimizing an estimation.
In converting between compass azimuths and angles in the Cartesian
plane, it is customary to equate North with the positive y
direction and East with the positive x direction. Standard angles
in the Cartesian plane are measured counter-clockwise from the
positive x axis. Under these conventions, the azimuth A (in
degrees) and standard angle .theta. (also in degrees) are related
by .theta.=90-A A=90-.theta. If the mobile A moves a distance of r
at an azimuth of A, the x and y components of this movement are
d.sub.x=r cos.theta.=r sin A d.sub.y=r sin.theta.=r cos A Within
the virtual constellation, the position of mobile unit k at time
t.sub.1 is (X.sub.k(t.sub.1),y.sub.k(t.sub.1)) and the position at
time t.sub.2 is (X.sub.k(t.sub.2),y.sub.k(t.sub.2)).
Referring to FIG. 8, in step 302 the position processing module 105
generates a vector d.sub.a representative of the apparent movement
of the mobile k (such as the mobile A) as evidenced by changes in
the virtual constellation, where
d.sub.a=x.sub.k(t.sub.2)-x.sub.k(t.sub.1),
y.sub.k(t.sub.2)-y.sub.k(t.sub.1) (9)
In step 304, the position processing module 105 generates a vector
d.sub.m representative of the measured movement of the mobile k
where the mobile k has moved a distance of r at an azimuth of A,
such that d.sub.m=r.sub.k sin A.sub.k, r.sub.k cos A.sub.k (10)
In a preferred embodiment of the present invention, the frequency
and duration of opportunities to adjust the yaw of the PRA
constellations will vary. A yaw adjustment opportunity occurs
whenever there are intervals of time, e.g., several seconds, over
which one or more individuals with mobiles perform regular movement
while several other individuals with mobiles are not moving. The
movement assessment module monitors movement status of the
individual at any instant and categorizes the status as: (1) not
moving; (2) regular movement for which a direction and a distance
can be measured with high confidence; (3) quasi-regular movement
for which a direction and distance can be measured with reduced
confidence; and (4) irregular movement for which direction and/or
distance cannot be reliably measured. For example, an electronic
compass of an individual measures whether an individual regularly
moves in a certain direction. The position of this individual
relative to the non-moving individuals is determined at the
beginning and the end of the regular movement interval. These two
positions define the beginning and end of the individual's line of
apparent regular movement, or movement vector ("MV"), through the
fixed background of the constellation. Overall, several different
azimuths and movement vectors can be obtained. If all of the
movement measurements were perfect, one azimuthal rotation of the
virtual constellation would bring each of the movement vectors into
alignment with its corresponding measured azimuth. In reality, the
measurements will not be perfect and each MV azimuth pair may
indicate a different amount of azimuth rotation is needed to bring
the PRA constellation into alignment.
In still a further preferred embodiment, the movement assessment
module includes an inclinometer which collects information to
permit the movement assessment module to distinguish between the
individuals' movements in erect and prone positions.
Referring again to FIG. 8, in step 306, the position processing
module 105 determines the alignment relationship between the
apparent movement and measured movement vectors. If the virtual
constellation is properly oriented with respect to the actual
deployment, the two movement vectors are parallel to each other. If
the virtual constellation has been oriented with respect to the
horizontal plane, but not with respect to azimuth, then the two
movement vectors can be brought into alignment by rotating the
virtual constellation around the z axis through an angle of .psi..
It is a well known result from analytic geometry that the
relationship between the vectors can be expressed as
d.sub.aT.sub.z=d.sub.m where
.function..function..times..times..function..function..times..times..time-
s..times..times..times..times..times..times..times..times..psi..times..tim-
es..psi..times..times..psi..times..times..psi. ##EQU00017## This
result can be extended to the case of k mobiles moving during the
time interval from t.sub.1 to t.sub.2: D.sub.aT.sub.z=D.sub.m (11)
where
.function..function..function..function..function..function..function..fu-
nction..function..function..function..function..times..times..times..times-
..times..times..times..times..times..times..times..times..times..times..ti-
mes..times..times..times..times..times..psi..times..times..psi..times..tim-
es..psi..times..times..psi. ##EQU00018## When D.sub.a and D.sub.m
are known, it is possible to use least squares techniques to solve
for T.sub.z yielding
##EQU00019## When solved in this unconstrained form, the
constraints implied by Equation (12) of a=d, c=-b and
a.sup.2+b.sup.2=1 may not be enforced. To eliminate redundant
elements in T.sub.z, Equation (11) can be reformulated such that
the rotation matrix becomes a 2-element column vector:
C.sub.at.sub.z=C.sub.m (13) where
.times..times..psi..times..times..psi..function..function..function..func-
tion..function..function..function..function..function..function..function-
..function..function..function..function..function..function..function..fu-
nction..function..function..function..function..function..times..times..ti-
mes..times..times..times..times..times..times..times..times..times..times.-
.times..times..times..times..times. ##EQU00020## Least squares
methods can be used to solve Equation (13) for t.sub.z as:
t.sub.z=[C.sub.a.sub.TC.sub.a].sup.-1C.sub.a.sup.TC.sub.m which
yields
##EQU00021## As a=cos.psi. and b=sin.psi., in step 308, the
position processing module 105 determines the angle .psi. by which
the virtual constellation must be rotated as
.psi..function.>.pi.<.pi.>.function..pi.<.ltoreq..function..p-
i.<> ##EQU00022##
FIGS. 10A 10D illustrate changes to the mirror image virtual
constellations of the group of mobiles of FIG. 2, which have been
determined and horizontally oriented in accordance with the present
invention based on movement measurements made during a yaw
adjustment opportunity and which lead to resolution of the
ambiguity in the virtual constellations in accordance with the
present invention. Assume, for example, that the left-hand image in
FIG. 10A is the correct one, but the position processing module has
not performed the steps of the process 300 to determine which image
of FIG. 10A is correct. A yaw adjustment opportunity occurs, for
example, when the mobile A moves a distance at a bearing of 90
degrees as measured by the electronic compass contained in the
mobile A. This movement of the mobile A results in new range
measurements for links AC and AB, producing the two movement AC and
AB vectors and the two constellation images as shown in FIG. 10B.
The two constellation images in FIG. 10 B, however, still exhibit
mirror-image symmetry. FIG. 10C shows the two constellation images
rotated so that each movement vector points to the right to signify
the yaw adjusted versions of these constellation images. A second
yaw adjustment opportunity occurs when the mobile B moves some
distance at a bearing of zero degrees as measured by its electronic
compass. This movement results in new range measurements for links
BC and BA, producing the movement vectors and the two constellation
images as shown in FIG. 10D. The movement vector in the left-hand
image in FIG. 10D points North and is consistent with the bearing
measured by the compass of the mobile B. The movement vector in the
right-hand image points South and conflicts with the measured
bearing, thus allowing the right-hand image to be rejected as
incorrect.
In accordance with a preferred embodiment of the present invention,
a movement vector can only be determined for mobiles engaged in
regular or quasi-regular movement. In a preferred embodiment, the
position processing module accounts for the circumstance where the
pattern of movements exhibited by the group of mobiles is such that
yaw adjustment opportunities occur very infrequently. If too much
time passes without a yaw adjustment, the position processing
module declares the orientation of the virtual constellation stale
and, therefore, unsuitable for deriving absolute bearing
information for display to individual members of the group.
Although the relative positions of nearby individuals still can be
displayed under these conditions, the relative positions
information in these displays is not tied to absolute directions
and, instead, is referenced to the apparent direction of the
movement vector for the individual wearing the display. Thus, if a
mobile is not moving, or is engaged in movement that the movement
assessment module deems to be irregular, the most recent
satisfactory movement vector is retained as the reference until
such time that it becomes possible to compute a new movement
vector.
In a preferred embodiment, the position display module 106
expresses the relative positions of the mobiles of the networked
group in the form of a compass bearing and relative distances from
each mobile to all other mobiles within the networked group. In a
further preferred embodiment, the position display module 106,
based on the computed relative positions, determines absolute
positions of the mobiles relative to Universal Transverse Mercator
coordinates or latitude and longitude.
In a further preferred embodiment, the mobile of the present
invention includes long-haul radio communication capabilities at
the data transceiver module, as known in the art, and communicates
the computed relative position information to another
communications device, such as a remotely located communications
base unit.
In a further preferred embodiment, the mobile 101 is a benchmark
unit including full GPS capability. The benchmark mobile is
preferably deployed in locations, such as vacant lots or rooftops,
that have good visibility of a GPS constellation. The benchmark
mobile uses its GPS capability, as well known in the art, to
determine its position with respect to both latitude and longitude
and with respect to the other team members based on the relative
position information provided by any of the mobiles of the group.
Based on this information, the benchmark mobile computes the
absolute position of each team member relative to the
benchmark.
In a preferred embodiment where a group of networked mobiles
contains fewer than four mobiles, the group must include a
benchmark mobile such that the total of mobiles plus benchmark
mobiles is at least four to provide that the relative positions can
be computed in accordance with the present invention.
In a preferred embodiment where one of the mobiles in a group of
networked mobiles of the preset invention is a benchmark mobile
which is intentionally placed in a fixed position, the benchmark
mobile provides an additional reference point that aids the other
mobiles to determine their relative positions as they maneuver. If
the GPS capabilities of the benchmark mobile are not available for
use, the benchmark mobile provides a stationary node in the
constellation to aid in the smooth evolution of the virtual
constellation as the true deployment undergoes rapid changes. In
another preferred embodiment, a benchmark mobile is placed at a
nexus of propagation paths of the group of mobiles and relays data
and ranging signals between mobiles that otherwise are unable to
communicate with or range each other. For example, a benchmark
mobile would be placed at a turn in a tunnel complex being searched
by a squad of soldiers.
In a further preferred embodiment, the benchmark mobile contains
long-haul radio communication capabilities for transmitting the
computed relative locations of the mobiles of the group to a remote
command post.
Although preferred embodiments of the present invention have been
described and illustrated, it will be apparent to those skilled in
the art that various modifications may be made without departing
from the principles of the invention.
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